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A new method for aspherical surface fitting with large-volume datasets

Article dans une revue avec comité de lecture
Author
EL HAYEK, Nadim
NOUIRA, Hichem
ANWER, Nabil
6862 École normale supérieure - Cachan [ENS Cachan]
DAMAK, Mohamed
ccGIBARU, Olivier
178374 Laboratoire des Sciences de l'Information et des Systèmes : Ingénierie Numérique des Systèmes Mécaniques [LSIS- INSM]

URI
http://hdl.handle.net/10985/8647
DOI
10.1016/j.precisioneng.2014.06.004
Date
2014
Journal
Precision Engineering

Abstract

In the framework of form characterization of aspherical surfaces, European National Metrology Institutes (NMIs) have been developing ultra-high precision machines having the ability to measure aspherical lenses with an uncertainty of few tens of nanometers. The fitting of the acquired aspherical datasets onto their corresponding theoretical model should be achieved at the same level of precision. In this article, three fitting algorithms are investigated: the Limited memory-Broyden-Fletcher-Goldfarb-Shanno (L-BFGS), the Levenberg–Marquardt (LM) and one variant of the Iterative Closest Point (ICP). They are assessed based on their capacities to converge relatively fast to achieve a nanometric level of accuracy, to manage a large volume of data and to be robust to the position of the data with respect to the model. Nev-ertheless, the algorithms are first evaluated on simulated datasets and their performances are studied. The comparison of these algorithms is extended on measured datasets of an aspherical lens. The results validate the newly used method for the fitting of aspherical surfaces and reveal that it is well adapted, faster and less complex than the LM or ICP methods.

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